Hi Joseph
Dear Gavin, Loet and Colleagues, Gavin raises a fair question as to the reasons for my objection to the use of category theory with respect to information. My answer is that it suffers from the same limitations as standard truth-functional logic, set theory and mereology: Logic: absolute separation of premisses and conclusion Set Theory: absolute separation of set and elements of the set Mereology: absolute separation of part and whole Category Theory: exhaustivity and absolute separation of elements of different categories. (The logics of topoi are Boolean logics). >From my limited working with Category Theory, it covers all the aspects you mention above, the logic by the subobject classifier, sets as objects, plus the arrows as functions. Associativity and identity as parts and wholes, plus the axioms of a Topos, which is part (is the part of the whole) of an object etc. (quantity, quality, variety, truth testing, unbounded-ness) The whole point of category theory is to be able to map dynamical systems. For complex process phenomena such as information, I don't understand what's the complex part of information. involving complementarity, overlap or physical interactions between elements, these doctrines fail. The "mathematical conceptualization" they provide does not capture the non-Markovian aspects of the processes involved for which no algorithm can be written. If any algebra is possible, it must be a non-Boolean one, something like that used in quantum mechanics extended to the macroscopic level. Is this not the whole point of Category theory. Regards Gavin I have proposed a new categorial ontology in which the key categorial feature is NON-separability. This concept would seem to apply to some of the approaches to information which have been proposed recently, e.g. those of Deacon and Ulanowicz. I would greatly welcome the opportunity to see if my approach and its logic stand up to further scrutiny. As Loet suggests, we must avoid confounding such a (more qualitative) discourse with the standard one and translate meaningfully between them. However this means, as a minimum, accepting the existence and validity of both, as well as the possibility in principle of some areas of overlap, without conflation. Best, Joseph ----- Original Message ----- From: Gavin Ritz To: 'Joseph Brenner' Sent: Tuesday, October 18, 2011 10:45 AM Subject: RE: [Fis] Chemo-informatics as the source of morphogenesis - bothpractical and logical. Hi there Joseph This takes us back to the question of the primacy of quantitative over qualitative properties, or, better, over qualitative + quantitative properties. Is this not a good reason to use category theory and a Topos (part of an object), does not the axiom of "limits" and the axiom of "exponentiation- map objects" deal philosophically with "quantity and limit" and "quality and variety" concepts respectively. Is this not the goal of category theory to explain the concepts in a conceptual mathematical way. Regards Gavin This for me is the real area for discussion, and points to the need for both lines being pursued, without excluding either. ----- Original Message ----- From: Gavin Ritz <mailto:garr...@xtra.co.nz> To: 'Joseph <mailto:joe.bren...@bluewin.ch> Brenner' Sent: Tuesday, October 18, 2011 10:45 AM Subject: RE: [Fis] Chemo-informatics as the source of morphogenesis - bothpractical and logical. Hi there Joseph This takes us back to the question of the primacy of quantitative over qualitative properties, or, better, over qualitative + quantitative properties. Is this not a good reason to use category theory and a Topos (part of an object), does not the axiom of "limits" and the axiom of "exponentiation- map objects" deal philosophically with "quantity and limit" and "quality and variety" concepts respectively. Is this not the goal of category theory to explain the concepts in a conceptual mathematical way. Regards Gavin This for me is the real area for discussion, and points to the need for both lines being pursued, without excluding either.
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